factor: new applet

thus far only able to factor up to ULLONG_MAX

function                                             old     new   delta
factor_main                                            -     378    +378
packed_usage                                       31427   31502     +75
applet_names                                        2590    2597      +7
applet_main                                         1500    1504      +4
------------------------------------------------------------------------------
(add/remove: 2/0 grow/shrink: 3/0 up/down: 464/0)             Total: 464 bytes

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>

1 files changed, 112 insertions, 0 deletions

diff --git a/coreutils/factor.c b/coreutils/factor.c
new file mode 100644
index 000000000..0f838a735
--- /dev/null
+++ b/coreutils/factor.c
@@ -0,0 +1,112 @@
+/*
+ * Copyright (C) 2017 Denys Vlasenko <vda.linux@googlemail.com>
+ *
+ * Licensed under GPLv2, see file LICENSE in this source tree.
+ */
+//config:config FACTOR
+//config:       bool "factor"
+//config:       default y
+//config:       help
+//config:         factor factorizes integers
+
+//applet:IF_FACTOR(APPLET(factor, BB_DIR_USR_BIN, BB_SUID_DROP))
+
+//kbuild:lib-$(CONFIG_FACTOR) += factor.o
+
+//usage:#define factor_trivial_usage
+//usage:       "NUMBER..."
+//usage:#define factor_full_usage "\n\n"
+//usage:       "Print prime factors"
+
+#include "libbb.h"
+
+#if ULLONG_MAX == (UINT_MAX * UINT_MAX + 2 * UINT_MAX)
+/* "unsigned" is half as wide as ullong */
+typedef unsigned half_t;
+#define HALF_FMT ""
+#elif ULLONG_MAX == (ULONG_MAX * ULONG_MAX + 2 * ULONG_MAX)
+/* long is half as wide as ullong */
+typedef unsigned long half_t;
+#define HALF_FMT "l"
+#else
+#error Cant find an integer type which is half as wide as ullong
+#endif
+
+static void factorize(const char *numstr)
+{
+        unsigned long long N, factor2;
+        half_t factor;
+        unsigned count3;
+
+        /* Coreutils compat */
+        numstr = skip_whitespace(numstr);
+        if (*numstr == '+')
+                numstr++;
+
+        N = bb_strtoull(numstr, NULL, 10);
+        if (errno)
+                bb_show_usage();
+
+        printf("%llu:", N);
+
+        if (N < 4)
+                goto end;
+        while (!(N & 1)) {
+                printf(" 2");
+                N >>= 1;
+        }
+
+        count3 = 3;
+        factor = 3;
+        factor2 = 3 * 3;
+        for (;;) {
+                unsigned long long nfactor2;
+
+                while ((N % factor) == 0) {
+                        N = N / factor;
+                        printf(" %u"HALF_FMT"", factor);
+                }
+ next_factor:
+                /* (f + 2)^2 = f^2 + 4*f + 4 = f^2 + 4*(f+1) */
+                nfactor2 = factor2 + 4 * (factor + 1);
+                if (nfactor2 < factor2) /* overflow? */
+                        break;
+                factor2 = nfactor2;
+                if (factor2 > N)
+                        break;
+                factor += 2;
+                /* Rudimentary wheel sieving: skip multiples of 3:
+                 * Every third odd number is divisible by three and thus isn't a prime:
+                 * 5  7  9  11  13  15  17 19 21 23 25 27 29 31 33 35 37...
+                 * ^  ^     ^   ^       ^  ^     ^  _     ^  ^     _  ^ (^primes)
+                 */
+                --count3;
+                if (count3 == 0) {
+                        count3 = 3;
+                        goto next_factor;
+                }
+        }
+ end:
+        if (N > 1)
+                printf(" %llu", N);
+        bb_putchar('\n');
+}
+
+int factor_main(int argc, char **argv) MAIN_EXTERNALLY_VISIBLE;
+int factor_main(int argc UNUSED_PARAM, char **argv)
+{
+        //// coreutils has undocumented option ---debug (three dashes)
+        //getopt32(argv, "");
+        //argv += optind;
+        argv++;
+
+        if (!*argv)
+                //TODO: read from stdin
+                bb_show_usage();
+
+        do {
+                factorize(*argv);
+        } while (*++argv);
+
+        fflush_stdout_and_exit(EXIT_SUCCESS);
+}